Simple equations, pre algebra solving equations

PRE ALGEBRA EQUATIONS - What are Equations?

Equations have equal signs x + 2 = 4, this is an equation with one variable x
Equations can have several terms, 2x + 3x + 4x + x = 36
Equations can have terms in brackets 2(1x + 3x + x) = 16

In order to solve equations, we solve for x (the variable can be any letter). To do so we must get the variable on one side of the equation, and the constants (numbers) on the other side.

One we have our answer, or solved for x, we then verify our answer, this confirms we have the correct answer. In Algebra, you can be asked to solve the equations for the variable, or to solve the equation.

x + 2= 4
An equation has two sides - Left side x + 2, and everything to the right of the equal sign, =, is the Right of the equation, 4

There are 4 Types of Equations
Addition Subtraction Multiplication Division

And 4 Methods Used to Solve Them



If your equation is minus, then you use the addition method to solve
If your equation is addition, then you use the subtraction method to solve
If your equation is multiplication, then you use the divide method to solve
If your equation is division, then you use multiply method to solve

To solve With the Addition Method: EXAMPLE


x - 13 = 36 In this equation we must solve for x

x - 13 = 36 As this equation has minus 13, we must add 13 to solve, the +13 is added to each equation side
x - 13 + 13 = 36 + 13
x = 49, the -13 and + 13 cancel each other, so you now have x-0, and add 36 and 13 equals 49
x = 49 For this equation x equals 49, the answer is 49

Then you can verify your answer
x - 13 = 36
49 - 13 = 36 Just add the answer you got to see if it solves the equation, 49 minus the 13 equals 36
36 = 36 Both sides are the same - You verified that you have the correct answer

PRACTICE EQUATIONS

Practice Solving Algebra Equations - Addition Method

x - 11 = 31
x - 5 = 15
x - 4 = 22
x - 3 = 12
x - 1 = 1




ANSWERS With Explanations

x - 11 = 31 To solve this equation, we use the addition method, because we solve using the opposite of the equation
x - 11 + 11 = 31 + 11
Add +11 to each side of the equation
x = 42 As -11 and +11 cancel each other, we get x = and then 31 + 11 add these numbers x = 42
x = 42 42 is the answer
Verify your answer
x - 11 = 31
42 - 11 = 31 Just add the answer you got to see if it solves the equation problem correctly
31 = 31
You know the answer is correct

x - 5 = 15
x - 5 + 5 = 15 + 5 use the addition method, add to each side of the equation +5
x = 20 The -5 +5 cancel each other, and 15 plus 5 is 20, x = 20
x = 20, the answer is 20 Now to verify your answer add your answer to the equation variable x
20 - 5 = 15
15 = 15 Both sides of the equation are equal, your answer is correct

x - 4 = 22
x - 4 + 4 = 22 + 4
x = 26
Answer is 26
26 - 4 = 22 Now verify your answer, add your answer to the equation variable x
22 = 22 Both sides of the equation are equal, your answer is correct

x - 3 = 12
x - 3 + 3 = 12 + 3
x = 15
Answer 15 Now verify your answer
15 - 3 = 12 Add your answer to the equation variable x
12 = 12 Both sides of the equation are equal, your answer is correct

x - 1 = 1
x - 1 + 1 = 1 + 1
x = 2
Answer 2 Now verify your answer
2 - 1 = 1
1 = 1 Both sides of the equation are equal, your answer is correct



To solve With the Subtraction Method: EXAMPLE


x + 6 = 15 In this equation we must solve for x

x + 6 = 15 As this equation has +6, we must add -6 to each side of the equation
x + 6 - 6 = 15 - 6
x + 0 = 9, the +6 and -6 cancel each other x + 0, and 15 minus 6 equals 9
x = 9, for this equation x = 9, the answer is 9

Then you can verify your answer
x + 6 = 15
9 + 6 = 15 Just add the answer you got to see if it solves the equation, 9 + 6 equals 15
15 = 15 Both sides are the same - You verified that you have the correct answer


Practice Solving Algebra Equations - Subtraction Method

x + 6 = 31
x + 11 = 15
x + 10 = 22
x + 6 = 12




ANSWERS With Explanations

x + 6 = 31
To solve,use the opposite method of the equation, this equation is using addition method, so we use subtraction method
x + 6 -6 = 31 - 6 Subtract 6 from each side of the equation
x = 25, +6 and -6 cancel each other x =
x = 25 Answer 25 Now verify your answer, replace x in the equation with 25, both sides should equal same
25 + 6 = 31
31 = 31 Both sides equal each, your answer is correct

x + 11= 15
 x + 11- 11 = 15 - 11 Subtract 11 from each side of the equation
x = 4 Now verify your answer, replace x in the equation with 4, both sides should equal same
4 + 11 = 15
15 = 15 Both sides equal each, your answer is correct

x + 10 = 22
 x + 10 - 10 = 22 - 10 Subtract 10 from each side of the equation
x = 12 verify your answer, replace x in the equation with 12 both sides should equal same
12 + 10 = 22
22 = 22 Both sides equal each, your answer is correct.

x + 6= 12
 x + 6 - 6 = 12 - 6 Subtract 6 from each side of the equation
x = 6 Verify your answer, replace x in the equation with 6, both sides should equal same
6 + 6 = 12
12 = 12 Both sides equal each, your answer is correct


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